{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hwB30 - ENEE 241 02 HOMEWORK ASSIGNMENT 30 Due Mon 04/28...

This preview shows pages 1–2. Sign up to view the full content.

ENEE 241 02* HOMEWORK ASSIGNMENT 30 Due Mon 04/28 Each of the infinite sequences x = x [ · ], y = y [ · ] and u = u [ · ] (shown below) contains seven nonzero terms. 1 3 x n = 0 2 4 1 3 y n = 0 2 4 1 3 u n = 0 2 4 (i) (3 pts.) Express u [ · ] as a linear combination of seven time-shifted impulses δ [ · - m ]. (ii) (2 pts.) Express each of x [ · ] and y [ · ] in terms of u [ · ]. (iii) (3 pts.) Express each of X ( e ) and Y ( e ) in terms of U ( e ). Write down the expressions for | X ( e ) | and | Y ( e ) | in terms of | U ( e ) | . How are X ( e ) and Y ( e ) related to U ( e )? (iv) (4 pts.) In MATLAB notation, define a column vector a such that the command fft(a) (alone) generates U ( e ) at 1,024 equally spaced frequencies in [0 , 2 π ). Repeat for X ( e ) and Y ( e ). (v) (4 pts.) Express U ( e ) in the form U ( e ) = e - jωm F ( ω ) , where F ( ω ) is a real-valued sum of cosines. (vi) (4 pts.) Define the signal z [ · ] = u [ · ] - u [ · - 1] - δ [ · - 4] + δ [ · - 8]. Find Z ( e ) and express Z ( e ) in the form Z ( e ) = je - jωm F ( ω ) , where F ( ω ) is a real-valued sum of sines. Solved Examples S 30.1 ( P 4.1 in textbook). (i) Sketch the signal sequence x [ n ] = δ [ n + 2] - δ [ n + 1] + 5 δ [ n ] - δ [ n - 1] + δ [ n - 2] and write an expression for its discrete-time Fourier transform

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hwB30 - ENEE 241 02 HOMEWORK ASSIGNMENT 30 Due Mon 04/28...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online